BEIRUT — A new rebel offensive around the Syrian capital has demonstrated the insurgents’ strengths after six months of combat in the Damascus region. But from afar it’s hard to gauge how close the rebels are to penetrating the central city or to capturing and holding new ground.

As in the country’s north, the rebels around Damascus have made gains against government bases, capturing weapons and demonstrating an ability to shoot down some of the government’s aircraft. But their advance has been slow in areas that are loyal to the government, and the government’s advantages of artillery and air power remain important factors in slowing the rebels.

Insurgents forced the closure of the Damascus airport, which lies several miles outside the city, last week for the first time. But the extent to which the fighting affected the airport itself — or merely the road leading to it — remains unclear.

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Residents of the capital report disunion in the rebel ranks and instances of infighting between groups. Some of those fights appeared to be related to ideological splits, residents said, while others appeared to be battles over territory.

As in other parts of the country, Islamist rebel groups appear to be leading the fight in Damascus, including fighters from Jabhat al-Nusra, or the Nusra Front, a group that U.S. officials say has ties to al-Qaida and that the United States said Monday it would designate a foreign terrorist group.

Living conditions in the capital have deteriorated, with bread and heating oil in short supply. Residents reached by phone said electricity was available for only six to 12 hours a day, depending on the neighborhood. That’s a marked difference from the beginning of the rebel offensive six months ago, when gasoline shortages were being felt but the capital otherwise was functioning.

In November, the greatest number of people killed in Syria died in and around Damascus — at least the third month in a row that was the case, according to statistics compiled by Syrian human rights groups. The fighting has left districts at the edge of the capital, and some within it, in ruins.

Residents say rebels appeared to be trying to consolidate positions on the eastern and western sides of the city, in order to press the military from two sides.

Former residents of Daraya, a suburb southwest of Damascus that had become a rebel stronghold before a government offensive in late August, reported that fighting had destroyed most of the area and that rebels were the only people who remained in the district.

In Yarmouk, a district that once was home to about half a million people, shelling has destroyed many neighborhoods. The fighting there displaced many people for a second time, as they’d fled there from other parts of the country that were less safe. Fighting continues in the neighborhoods around Yarmouk, as well as in northeastern parts of the city leading to the long-restive suburb of Douma.

Direct clashes between rebels and a Palestinian militia allied with the government demonstrate the rift among Palestinians, a significant population in Yarmouk. Many Palestinian youths have supported the rebellion against President Bashar Assad, while older Palestinians have remained loyal to Assad. The tensions have sparked repeated clashes, with neither side taking clear control of the area.

In recent weeks, government airpower has been used increasingly in the battles around Damascus, suggesting an increase in rebel numbers and a greater control of some areas. But the airpower often appears ineffective, with helicopter crews resorting to rolling bombs out of their aircraft, in some cases explosives-packed canisters that Syrians refer to as “barmeels,” Arabic for “barrel.” One theory is that the tactic allows helicopter pilots to fly at heights greater than those necessary to fire missiles, allowing them to avoid anti-aircraft fire.

In a new twist, pictures were posted online Sunday claiming to show what appeared to be naval mines dropped from a government helicopter in Daraya. There was no explanation for why the military would have dropped such munitions.

Residents of Damascus said they saw little evidence of greater coordination among rebel groups fighting in the city than there had been in July.

The insurgents have worked quickly in past months to coordinate actions, and fighters in the eastern province of Deir al-Zour said last month that some of their battalions from the area already were fighting in Damascus. Others said that when the government had been driven from Deir al-Zour, Damascus would become their focus.

The split between Islamist rebel groups who refer to themselves as mujahedeen and those who say they’re fighting under the banner of the secular Free Syrian Army has become increasingly clear in recent months.